What is 16ln(5)-4ln(2) ?

The solution to 16ln(5)-4ln(2) is ln((5^{16})/(16))

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simplify 16ln(5)-4ln(2)

simplify

16 ln (5) - 4 ln (2)

ln (\frac{5 ^{16}}{16})

Decimal Notation

22.97841 \dots

Solution steps

16 ln (5) - 4 ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

16 ln (5) = ln (5^{16})

= ln (5^{16}) - 4 ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (2) = ln (2^{4})

= ln (5^{16}) - ln (2^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (5^{16}) - ln (2^{4}) = ln (\frac{5 ^{16}}{2 ^{4}})

= ln (\frac{5 ^{16}}{2 ^{4}})

2^{4} = 16

= ln (\frac{5 ^{16}}{16})

\frac{( 1 )}{( x ( ln ^{2} ( x ) + ln ( x ) + 1 ) )}

ln (\frac{0.49}{0.945})

ln (t^{x i} (1 - t)^{1 - x i})

lo g_{2} (\frac{y}{z})

- 0.04 - \frac{0.257}{2} ln (\frac{0.01}{0.6})